In Mark 2:1-12 we read:
And when he returned to Capernaum after some days, it was reported that he was at home. And many were gathered together, so that there was no more room, not even at the door. And he was preaching the word to them. And they came, bringing to him a paralytic carried by four men. And when they could not get near him because of the crowd, they removed the roof above him, and when they had made an opening, they let down the bed on which the paralytic lay. And when Jesus saw their faith, he said to the paralytic, “Son, your sins are forgiven.” Now some of the scribes were sitting there, questioning in their hearts, “Why does this man speak like that? He is blaspheming! Who can forgive sins but God alone?” And immediately Jesus, perceiving in his spirit that they thus questioned within themselves, said to them, “Why do you question these things in your hearts? Which is easier, to say to the paralytic, ‘Your sins are forgiven,’ or to say, ‘Rise, take up your bed and walk’? But that you may know that the Son of Man has authority on earth to forgive sins” - he said to the paralytic - “I say to you, rise, pick up your bed, and go home.” And he rose and immediately picked up his bed and went out before them all, so that they were all amazed and glorified God, saying, “We never saw anything like this!”
Anyone can say your sins are forgiven. I mean, the pope can say he's forgiving sins for anyone who retweets him, for cryin' out loud. (Side note - is Tweetzel the saddest Roman episode you can remember? They used to be able to extort money for 'indulgences', now they're reduced to RTs? Pathetic.) Anyone who wants can claim to forgive anyone's sins - who can check it? How would you falsify?
But who would claim to be able to heal the paralyzed? What could be more easily falsifiable? You say you can heal - well, heal! And here, Jesus does exactly that. He tells a paralytic to get up and walk, and he does!
Now, commanding a paralyzed man to walk is beyond amazing. But how does it prove that Jesus can also forgive sins? Jesus says the healing is proof of his authority to forgive (see also here). Is it, and if so, how?
One response is that the visible, unquestionable power on display in healing gives confidence that we can trust him for the invisible power he claims. If he can do this humanly impossible act you can see, why can't he also do the humanly impossible that you can't see?
I think there's something more to it, though. Why was the man paralyzed to begin with? Because of sin. Now I don't mean that in the Job's friends, John 9 kind of way, that he did a specific sin and was paralyzed as punishment. I mean it in the general sense - Adam sinned, and we were cursed, and so life is full of suffering and ends in death. We're sinners living in a broken, cursed world.
When Jesus heals, it isn't just a display of power, generally. When Jesus heals, and raises the dead, he is showing specifically the power to undo the effects of the curse. And if he can overpower the effects of the curse, he can overpower the cause - sin.
In Adam's sin, we were cursed and broken. In the second Adam's righteousness, the curse is broken and we are made new. When Jesus healed, he was pointing to the much greater healing he would perform through his righteous life, death and resurrection. Sin is forgiven, death is conquered, and we are reconciled to God.
20 minutes ago